Assignment 4

by

Jackson Huckaby

Below is an applet of a construction of a triangle with the orthocenter labeled as H. Try on your own to manipulate the triangle to come to some conclusions.

Things to search for:

i. When is the orthocenter inside the triangle?

ii. When is the orthocenter outside of the triangle?

This page uses **JavaSketchpad**, a World-Wide-Web component of *The Geometer's Sketchpad.* Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.

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Orthocenter

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i. When is my orthocenter outside of the triangle?

We see that by making the triangle an obtuse triangle, the orthocenter leaves the inside of the triangle.

ii. From part i, we can now gather that the orthocenter is inside of the triangle when the triangle is an acute triangle.

iii. From these two ideas, we can come to the conclusion that when the triangle is a right triangle then the orthocenter will lay on the vertex of the right angle.

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What other types of triangles can we try?

Isosceles Triangle:

Equilateral Triangle:

What we can notice in an equilateral triangle is that our orthocenter is also the same point as our incenter and circumcenter.

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